Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities, they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold ?cr such that minimizers for this variational problem exist if their power is bigger than ?cr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of [15] and [16].Comment: 49 pages, no figure

Human Factors in Design

This Grants Collection for Human Factors in Design was created under a Round One ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/engineering-collections/1000/thumbnail.jp

Cross-cultural study of obesity regarding socio-cultural attitudes on appearance involvement and appearance management behaviors through clothing: 20s-30s female plus-size consumers

Socio-cultural attitudes on obesity differently influence on formation of individual person\u27s body image, attitudes, and appearance management and involvement. Recently consumer market research on young female plus-size consumers clearly shows the increasing population of obesity and the changing social perception on the plus-size market from being negative to being somewhat positive

Discrete diffraction managed solitons: threshold phenomena and rapid decay for general nonlinearities

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities, they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions\u27 concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of [15] and [16]

Well-posedness of dispersion managed nonlinear Schr\"odinger equations

We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schr\"odinger equation with a large class of nonlinearities and arbitrary average dispersion on $L^2(\mathbb{R})$ and $H^1(\mathbb{R})$. Moreover, when the average dispersion is non-negative, we show that the set of nonlinear ground states is orbitally stable.Comment: 29 page

Simultaneous deletion of floxed genes mediated by CaMKIIa-Cre in the brain and in male germ cells: application to conditional and conventional disruption of Go-alfa

The Cre/LoxP system is a well-established approach to spatially and temporally control genetic inactivation. The calcium/calmodulin-dependent protein kinase II alpha subunit (CaMKIIα) promoter limits expression to specific regions of the forebrain and thus has been utilized for the brain-specific inactivation of the genes. Here, we show that CaMKIIα-Cre can be utilized for simultaneous inactivation of genes in the adult brain and in male germ cells. Double transgenic Rosa26+/stop-lacZ::CaMKIIα-Cre+/Cre mice generated by crossing CaMKIIα-Cre+/Cre mice with floxed ROSA26 lacZ reporter (Rosa26+/stop-lacZ) mice exhibited lacZ expression in the brain and testis. When these mice were mated to wild-type females, about 27% of the offspring were whole body blue by X-gal staining without inheriting the Cre transgene. These results indicate that recombination can occur in the germ cells of male Rosa26+/stop-lacZ::CaMKIIα-Cre+/Cre mice. Similarly, when double transgenic Gnao+/f::CaMKIIα-Cre+/Cre mice carrying a floxed Go-alpha gene (Gnaof/f) were backcrossed to wild-type females, approximately 22% of the offspring carried the disrupted allele (GnaoΔ) without inheriting the Cre transgene. The GnaoΔ/Δ mice closely resembled conventional Go-alpha knockout mice (Gnao−/−) with respect to impairment of their behavior. Thus, we conclude that CaMKIIα-Cre mice afford recombination for both tissue- and time-controlled inactivation of floxed target genes in the brain and for their permanent disruption. This work also emphasizes that extra caution should be exercised in utilizing CaMKIIα-Cre mice as breeding pairs.Fil: Choi, Chan-Il. Ajou University. School of Medicine; Corea del SurFil: Yoon, Sang-Phil. Ajou University. School of Medicine; Corea del SurFil: Choi, Jung-Mi. Ajou University. School of Medicine; Corea del SurFil: Kim, Sung-Soo. Ajou University. School of Medicine; Corea del SurFil: Lee, Young-Don. Ajou University. School of Medicine; Corea del SurFil: Birnbaumer, Lutz. National Institute of Environmental Health Sciences; Estados Unidos. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; ArgentinaFil: Suh-Kim. Haeyoung. Ajou University. School of Medicine; Corea del Su